Related papers: The Shilov boundary for a local operator system
In this paper we develop a boundary $\varepsilon$-regularity theory for optimal transport maps between bounded open sets with $C^{1,\alpha}$-boundary. Our main result asserts sharp $C^{1,\alpha}$-regularity of transport maps at the boundary…
In this paper we give conditions under which sub differential limits can be better estimated.
In this paper several new bounds for the \v{C}eby\v{s}ev functional involving $L_p$-norm are presented.
This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain.…
We get optimal lower bounds for the eigenvalues of the submanifold Dirac operator on locally reducible Riemannian manifolds in terms of intrinsic and extrinsic expressions. The limiting-cases are also studied. As a corollary, one gets…
We study a Dirichlet problem in the entire space for some nonlocal degenerate elliptic operators with internal nonlinearities. With very mild assumptions on the boundary datum, we prove existence and uniqueness of the solution in the…
In this paper, we introduce the magnetic Steklov operator on differential forms and show that the underlying boundary value problem is well-posed. Moreover, we show that an analogue of the Diamagnetic Inequality does not always hold for…
The aim of this paper is twofold: First, we characterize an essentially optimal class of boundary operators $\Theta$ which give rise to self-adjoint Laplacians $-\Delta_{\Theta, \Omega}$ in $L^2(\Omega; d^n x)$ with (nonlocal and local)…
We consider the question of convergence of a sequence of gradient flows defined on different Hilbert spaces. In order to give meaning to this idea, we introduce a notion of connecting operators. This permits us to generalize the concept of…
We develop a regularization operator based on smoothing on a locally defined length scale. This operator is defined on $L_1$ and has approximation properties that are given by the local regularity of the function it is applied to and the…
We obtain a new bound on the location of eigenvalues for a non-self-adjoint Schr\"odinger operator with complex-valued potentials by obtaining a weighted $L^2$ estimate for the resolvent of the Laplacian.
We study local controllability and optimal control problems for invertible discrete-time control systems. We present second order necessary conditions for optimality and sufficient conditions for local controllability. The conditions are…
In this paper we examine a natural operator system structure on Pisier's self-dual operator space. We prove that this operator system is completely order isomorphic to its dual with the cb-condition number of this isomorphism as small as…
We consider the optimal discrimination of bipartite quantum states and provide an upper bound for the maximum success probability of optimal local discrimination. We also provide a necessary and sufficient condition for a measurement to…
The local boundedness of classes of operators is analyzed on different subsets directly related to their Fitzpatrick functions and characterizations of the topological vector spaces for which that local boundedness holds is given in terms…
We consider Schr\"odinger operators of the form $H_R = - d^2/ d x^2 + q + i \gamma \chi_{[0,R]}$ for large $R>0$, where $q \in L^1(0,\infty)$ and $\gamma > 0$. Bounds for the maximum magnitude of an eigenvalue and for the number of…
The main goal of this note is to characterize the necessary and sufficient conditions for a composition operator to act between spaces of mappings of bounded Wiener variation in a normed-valued setting. The necessary and sufficient…
We present the set of axioms for topological space with the operation of boundary as primitive notion.
Boundedness of wave operators for Schr\"odinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive…
We consider a dilation operator on Besov spaces $(B^s_{r,t}(K))$ over local fields and estimate an operator norm on such a field for $s > \sigma_r = \text{max}\big(\frac{1}{r} -1,~0\big)$ which depends on the constant $k$ unlike the case of…